Consider a unity feedback system, as in the figure shown, with an integral compensator and open-loop transfer function G(s)=\frac{1}{s^{2}+3 s+2} Where {K}>0. The positive value of {K} for which there are exactly two poles of the unity feedback system on the {j} \omega axis is equal to (rounded off to two decimal places).

GATE Electronics and Communications (EC) 2019 Solved Paper

Question : 63 of 65

Marks: +1, -0

Consider a unity feedback system, as in the figure shown, with an integral compensator and open-loop transfer function

G(s)=\;{1}/{s^{2}+3 s+2}

Where

{K}>0

. The positive value of

{K}

for which there are exactly two poles of the unity feedback system on the

{j} ω

axis is equal to (rounded off to two decimal places).

Solution:

Overall

G_{C}(s)=\;{K}/{s(s^{2}+3 s+2)}

∴ q(s)=s^{3}+3 s^{2}+2 s+k=0

Auxiliary equation is

3 s^{2}+k=0

And for roots on imaginary axis

{s}^{1}

row = 0

∴ \;{6- {k}}/{3}=0

∴ {k}=6

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